Sums of Products of Bernoulli numbers of the second kind
Abstract
The Bernoulli numbers b0,b1,b2,.... of the second kind are defined by Σn=0∞ bntn=t(1+t). In this paper, we give an explicit formula for the sum Σj1+j2+...+jN=n, j1,j2,...,jN>=0bj1bj2...bjN. We also establish a q-analogue for Σk=0n bkbn-k=-(n-1)bn-(n-2)bn-1.
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